J. Am. Chem. Soc. 2001, 123, 1755-1759
1755
Quantum Mechanical Designs toward Planar Delocalized Cyclooctatetraene: A New Target for Synthesis Kim K. Baldridge* and Jay S. Siegel* Contribution from the San Diego Supercomputer Center, La Jolla, California 92093-0505, and Department of Chemistry, UniVersity of California-San Diego, La Jolla, California 92093-0358 ReceiVed September 14, 2000. ReVised Manuscript ReceiVed NoVember 17, 2000
Abstract: Ab initio and hybrid density functional quantum mechanical computation are applied to the structure and energetics of a series of annelated cyclooctatetraenes. Tetrakis-cyclobuteno, perfluorocyclobuteno or bicyclo[2.1.1]hexeno annelations result in planar structures with distinct exo and endo valence tautomers of the double bonded cycle. The contribution of each basic annelation to the exo/endo relative energy is estimated. An additivity scheme for approximating the energy of a mixed system is developed and compared to the quantum mechanical prediction. Bis bicyclic annelation to the a and d positions creates “valence tautomeric frustration” and strongly perturbs the molecular structure. This phenomenon leads to a general design for a planar cyclooctatetraenes where the “delocalized” diradicaloid state is the minimum energy form. These compounds are seen as excellent targets for chemical synthesis.
The standard view of cyclooctatetraene (1) is that of a molecule with a tub shape undergoing two dynamic processes: (I) tub-inversion and (II) valence-bond shifting (Figure 1).1-4 Colloquially, the bond-localized nonplanar structure of 1 is ascribed to “anti-aromatic” character of [4n]-annulenes in general. Given our recent success in using bicyclic annelations to create a bond-length alternate benzene,5,6 and related [4n+2]annulenes,7,8 it seemed worthy to apply similar annelation strategies in pursuit of planar symmetric cyclooctatetraene.9,10 The energy hypersurface of 1 is a double-welled potential in the tub-inversion, as well as in the bond-shift coordinate.11 The bond-localized nonplanar “tub” form (D2d) is the global minimum, and the planar delocalized D8h form is a saddle-point of relatively high energy (∼14 kcal/mol).12,13 In addition, the tub (D2d) or localized-flat (D4h) forms adopt a closed-shell singlet electronic configuration. The flat delocalized D8h form could be viewed as “triplet-aromatic;”14,15 however, a general phenomenon in “disjoint” singlet diradicals has been shown to stabilize the open-shell singlet in 1.16-18 On the basis of these (1) March, J. AdVanced Organic Chemistry, 2nd ed.; John Wiley and Sons: New York, 1986. (2) Paquette, L. Tetrahedron 1975, 31, 2855. (3) Paquette, L. Pure Appl. Chem. 1982, 54, 987. (4) Oth, J. F. M. Pure Appl. Chem. 1971, 25, 573. (5) Frank, N. L.; Baldridge, K. K.; Siegel, J. S. J. Am Chem. Soc. 1995, 117, 2102-2103. (6) Burgi, H. B.; Baldridge, K. K.; Hardcastle, K.; Frank, N. L.; Gantzel, P.; Siegel, J. S.; Ziller, J. Angew. Chem., Int. Ed. Engl. 1995, 34, 14541456. (7) Baldridge, K. K.; Siegel, J. S. Angew. Chem., Int. Ed. Engl. 1997, 36, 745-748. (8) Mitchell, R. H.; Chen, Y. S.; Iyer, V. S.; Lau, D. Y. K.; Baldridge, K. K.; Siegel, J. S. J. Am. Chem. Soc. 1996, 118, 2907-2911. (9) Ermer, O.; Kla¨rner, F.-G.; Wette, M. J. Am. Chem. Soc. 1986, 108, 4908. (10) Schleyer, P. v. R.; Jiao, H. J.; Sulzbach, H. M.; Schaefer, H. F. J. Am. Chem. Soc. 1996, 118, 2093-2094. (11) Garratt, P. J. Aromaticity; Wiley: New York, 1986. (12) Anet, F. A. L. J. Am. Chem. Soc. 1962, 84, 671. (13) Anet, F. A. L.; Bourn, A. J. J. Am. Chem. Soc. 1964, 86, 3576. (14) Baird, N. C. J. Am. Chem. Soc. 1972, 94, 4941-4948. (15) Gogonea, V.; Schleyer, P. v. R.; Schreiner, P. R. Angew. Chem., Int. Ed. 1998, 37, 1945-1948.
Figure 1. The tub-inversion (I) and valance-bond shift (II) processes in 1.
characteristic electronic states and the perturbations induced by bicyclic annelations, it is our contention that it should be possible to create a planar delocalized diradicaloid cyclooctatetraene. Computational Considerations All calculations have been carried out using the GAMESS,19 Gaussian98,20 and MOLPRO21 software packages, running on the hardware facilities at the San Diego Supercomputer Center, including a generous amount of time donated by Compaq Inc. The molecular (16) Hrovat, D. A.; Borden, W. T. J. Am. Chem. Soc. 1992, 114, 4, 58795881. (17) Wenthold, P. G.; Hrovat, D. A.; Borden, W. T.; Linberger, W. C. Science 1996, 272, 1456-1459. (18) Kato, S.; Lee, H.; Gareyev, R.; Wenthold, P.; Lineberger, W.; DePuy, C.; Bierbaum, V. J. Am. Chem. Soc. 1997, 119, 7863-7864. (19) Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.; Elbert, S. T.; Gordon, M. S.; Jensen, J. H.; Koseki, S.; Matsunaga, N.; Nguyen, K. A.; Su, S. J.; Windus, T. L.; Dupuis, M.; Montgomery, J. A. J. Comput. Chem. 1993, 14, 1347-1363. (20) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Robb, M. A.; Cheeseman, J. R.; Keith, T. A.; Petersson, G. A.; Montgomery, J. A.; Raghavachari, K.; Al-Laham, M. A.; Zakrzewski, V. G.; Ortiz, J. V.; Foresman, J. B.; Cioslowski, J.; Stefanov, B. B.; Nanayakkara, A.; Challacombe, M.; Peng, C. Y.; Ayala, P. Y.; Chen, W.; Wong, M. W.; Andres, J. L.; Replogle, E. S.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Binkley, J. S.; DeFrees, D. J.; Baker, J.; Stewart, J. P.; HeadGordon, M.; Gonzalez, C.; Pople, J. A. Gaussian 98, revision B.1; Gaussian, Inc.: Pittsburgh, PA, 1998.
10.1021/ja003383+ CCC: $20.00 © 2001 American Chemical Society Published on Web 02/02/2001
1756 J. Am. Chem. Soc., Vol. 123, No. 8, 2001 structures were determined using a variety of levels of theory to establish self-consistency in terms of basis sets as well as effects of dynamic correlation. Wave function-based methods were considered, specifically Hartree-Fock (HF), second-order Møller-Plesset perturbation theory,22 coupled cluster theory with all single and double substitutions augmented by a quasi-perturbative accounting of triple excitations (CCSD(T)),23 and conventional multiconfigurational SCF (MCSCF).24,25 Hybrid density functional theory (HDFT) methods, which constitute a known improvement over “pure” DFT methods via inclusion of the exact HF exchange based on Kohn-Sham orbitals,26 were also considered. The HDFT methods employed Becke’s three parameter hybrid exchange functional27 in combination with the Perdew and Wang 1991 gradient-corrected nonlocal correlation functional, B3PW91.28,29 The DZV(2d,p), DZ(2d,p), and DZV(2df,pd)30 double-ζ valence quality basis sets were employed. These basis sets include 2d (2df) polarization functions on all heavy atoms, and p (pd) polarization functions on hydrogen atoms. These levels of theory have been previously shown by us to be reliable for structural determination in these types of compounds.8 The nature of each stationary point was uniquely characterized by calculating and diagonalizing the matrix of energy second derivatives (Hessian) to determine the number of imaginary frequencies. This Hessian also provided the zero-point energy corrections used in the evaluation of the energetics. Stability checks were performed on the HF and HDFT wave functions.31,32 Molecular orbital contour plots, used as an aid in the discussion of the results, were generated using the program 3D-PLTORB (San Diego, 3D version: 1997), and depicted using QMView.33 The multiconfigurational self-consistent-field wave function (CASSCF) computations were used to investigate several of the analogues studied. These MCSCF computations24,25 were carried out using GAMESS, with the DZV(2d,p) basis set. An 8-electron-8-orbital active space was chosen [CASSCF(8,8)]. A modified virtual orbital computation34 was performed for improved starting orbitals. The multiconfiguration quasi-degenerate perturbation theory (MCQDPT) method35 was performed on top of the MCSCF for second order perturbation correction. This method is a multistate, as well as multireference perturbation theory. MCQDPT will recover dynamic correlation energy comparable to that of the CASPT2 methodology, and is thought to be potentially better for the prediction of singlet-triplet splittings. This latter point is a result of slightly different definition of the high-spin zeroth order functions.
Discussion Arguably, the nonplanarity of the tub conformation of cyclooctatetraene could come solely from angle strain, as a planar localized structure need not suffer antiaromatic destabi(21) H.-J. Werner; P. J. Knowles; R. D. Amos; A. Berning; D. L. Cooper; M. J. O. Deegan; A. J. Dobbyn; F. Eckert; C. Hampel; T. Leininger; R. Lindh; A. W. Lloyd; W. Meyer; M. E. Mura; A. Nicklass; P. Palmieri; K. Peterson; R. Pitzer; P. Pulay; G. Rauhut; M. Schutz; H. Stoll; A. J. Stone; P. R. Taylor; T. Thorsteinsson, MOLPRO, 98.1, 1998. (22) Møller, C.; Plesset, M. S. Phys. ReV. 1934, 46, 618-622. (23) Raghavachari, K.; Trucks, G. W.; Pople, J. A.; Head-Gordon, M. Chem. Phys. Lett. 1989, 157, 479. (24) Roos, B. O. In Methods in Computational Molecular Physics; Diercksen, G. H. F., Wilson, S., Eds.; D. Reidel Publishing: Dordrecht, 1983; pp 161-187. (25) Schmidt, M. W.; Gordon, M. S. Annu. ReV. Phys. Chem. 1998, 49, 233-266. (26) Kohn, W.; Sham, L. J. Phys. ReView 1965, 140, A1133-A1138. (27) Becke, A. D. J. Chem. Phys. 1993, 98, 5648-5652. (28) Perdew, J. P.; Chevary, J. A.; Vosko, S. H.; Jackson, K. A.; Pederson, M. R.; Singh, D. J.; Fiolhais, C. Phys. ReV. B 1992, 46, 66716687. (29) Perdew, J. P.; Burke, K.; Wang, Y. Phys. ReV. B 1996, 54, 1653316539. (30) Dunning, T. H., Jr.; Hay, P. J. Modern Theoretical Chemistry; Plenum: New York, 1976. (31) Bauernschmitt, R.; Ahlrichs, R. J. Chem. Phys. 1996, 104, 9047. (32) Seeger, R.; Pople, J. A. J. Chem. Phys. 1977, 66, 3045. (33) Baldridge, K. K.; Greenberg, J. P. J. Mol. Graphics 1995, 13, 6366. (34) Bauschlicher, C. W., Jr. J. Chem. Phys. 1980, 72, 880-885. (35) Nakano, H. J. Chem. Phys. 1993, 99, 7983-7992.
Baldridge and Siegel Table 1. HDFT Comparison of the Tautomeric (I/II) Structures and Energies for 2, 3, 4, 5, and 6a
I cmpd
C-Cexo
2 3 4 5 6
1.449 1.453 1.487/1.484 1.449 1.446
a
II
C-Cendo EI 1.356 1.365 1.334 1.355 1.364
0 2.3 0 32.7 13.6
C-Cexo
C-Cendo
1.331 1.335 1.358/1.361 1.339 1.336
1.484 1.487 1.449 1.496 1.493/1.479
EII Eannelation 17.2 0 7.2 0 0
4.3 0.6 8.2
Bond lengths are in Å and energies in kcal/mol.
lization. Opening the interior CCC angle to 135° from 120° would then result in a planar structure. Indeed, the crystal structure of perfluorotetracyclobutenocyclooctatetraene (2) has been reported as a flat molecule of ∼D4h symmetry.36 Our HDFT computations (B3PW91/DZ(2d,p)) of 2 and its parent hydrocarbon (3) also predict the minimum energy structure to be flat and D4h symmetric (Table 1), thus, demonstrating that modulation of bond angles by annelations can be used to control the planarity (structure coordinate I) of derivatives of 1.
Although 2 and 3 are planar, they remain D4h symmetric with strong bond length alternation (|δexo-endo| ) 9.3 and 15.2 pm, respectively) and leave open the question of the double-welled bond-shift coordinate (structure coordinate II). For these types of molecules, we can have two isomers differing only by the position of the double bonds with respect to the annelations (exo vs endo valence tautomers).37 The X-ray crystal structure of 2 displays the double bonds within the four-membered ring annelations, contrary to classical strain arguments,38 but consistent with our predictions on the basis of the electronic perturbations induced by such perfluorinations.39 Computations reveal two minima of D4h symmetry for 2 and 3. In accord with the experimental structures, tautomer I is lower in energy for 2, by 17.2 kcal/mol, and tautomer II is lower for 3, by 2.3 kcal/mol (cf. Table 1). Thus, the hydrocarbon shows a small preference to having the π bonds localized outside the annelations, whereas the energetic requirements for the fluorocarbon are substantially reversed. Assuming an equal contribution to the energy from each annelation, one would predict that each hydrocarbon annelation prefers exo double bonds by (36) Einstein, F. W. B.; Willis, A. C. J. Chem. Soc., Chem. Commun. 1981, 526. (37) It is interesting to note that the principal change in the two valance tautomers is a cooperative change of bond lengths. In that sense, some might consider this a form of bond stretch isomerism, where there are two minima along a geometrical coordinate dominated by bond length changes. (38) Stanger, A. J. Am. Chem. Soc. 1998, 120, 12034-12040. (39) Baldridge, K. K.; Siegel, J. S. J. Am. Chem. Soc. 1992, 114, 9583.
Planar Delocalized Cyclooctatetraene ∼0.6 kcal/mol, whereas the fluorocarbon annelations prefer endo double bonds by ∼4.3 kcal/mol. Applying a simple additivity scheme to 4, a mixed system with two hydrocarbon annelations and two fluorocarbon annelations, one finds two annelations favoring the exo tautomer by 0.6 kcal/mol and two favoring the endo isomer by 4.3 kcal/mol for an exo-endo energy difference of 7.4 kcal/mol in favor of the endo tautomer. These results, which come very close to those obtained from the computations for 4, show that the fluorocarbon annelations are dominant and encourage the use of this additivity scheme in future designs. Previously, we had touted the special character of bicycloannelations, especially the bicyclo[2.1.1]hexeno fragment, for controlling bond length alternation in annulenes.7,39 Computations on tetrakisbicyclo[2.1.1]hexenocyclooctatetraene (5) also predict a planar structure of D4h symmetry. In 5, the bond length alternation is more extreme than in 2 or 3, and the lower energy tautomer is of form II, paralleling the chemistry of 3. The energy difference between 5-I and 5-II (32.7 kcal/mol, or roughly 8-9 kcal/mol/annelation) is much greater than that for 3. As in test compound 4, we also calculated compound 6 in which the bicyclohexeno annelation is competed against the perflurocyclobuteno annelations. Here the additivity predicts the exo tautomer (6-I) in favor of the endo tautomer (6-II) by approximately 8-9 kcal/mol. The QM calculations indeed predict the exo form (6-I) as the favored tautomer, but by 13.6 kcal/ mol.
It would seem from these results that the bicycloannelation is able to induce a planar structure through angle deformations,40 but these annelations should also interact strongly with the π orbitals in the central ring.41-43 This supposition led us to ask whether bicyclic annelations could be placed so as to “frustrate” the valence tautomers and lead to a delocalized annulene (more precisely, could bicyclic annelation at bonds a and d result in a planar cyclooctatetraene ring with a single-well potential in the bond-shift coordinate). The design principle is clear, and the (40) The synthesis of 5 has been recently accomplished by Matsuura and Komatsu. Their crystallographically determined structure agrees well with our computational prediction, see: Matsuura, A.; Komatsu, K. J Am. Chem. Soc. 2001, 123, 1768-1769. (41) Gleiter, R.; Bischof, P.; Gubernator, K.; Christl, M.; Schwager, L.; Vogel, P. J. Org. Chem. 1985, 50, 5064-5069. (42) Jorgensen, W. L.; Borden, W. T. J. Am. Chem. Soc. 1973, 95, 66496654. (43) Jorgensen, W. L. J. Am. Chem. Soc. 1975, 97, 3082-3090. (44) A small out of plane mode indicates that the Cs structure sits on a flat hill. Optimization along that out of plane coordinate produces a minimum energy C1 structure 0.6 kcal/mol lower than the Cs structure.
J. Am. Chem. Soc., Vol. 123, No. 8, 2001 1757 Table 2. MCSCF and HDFT Structures for Singlet and Triplet 7 and 8a singlet
triplet
cmpd
Cs
C2ν
C2ν
7 B3PW91/DZ(2d,p) 7 MCSCF/DZV(2d,p) 8 B3PW91/DZ(2d,p)
1.454, 1.360, 1.451, 1.351, 1.470, 1.341, 1.508, 1.340 1.467, 1.357, 1.463, 1.350, 1.478, 1.343, 1.506, 1.322 1.454, 1.365, 1.439, 1.366, 1.482, 1.336, 1.508, 1.346
1.393, 1.435, 1.389, 1.410 1.396, 1.434, 1.393, 1.414 1.396, 1.439, 1.380, 1.425
1.390, 1.439, 1.383, 1.410 1.389, 1.454, 1.377, 1.419 1.393, 1.443, 1.373, 1.427
a Lengths are in Å starting from bond a-h; bold bond lengths are for the endo bonds.
Table 3. MCQDPT and HDFT Computed Relative (kcal/mol) Energetics for Structure 7 method B3PW91/DZ(2d,p) B3PW91/DZ(2d,p)+ZPE B3PW91/DZV(2df,pd)//B3PW91/DZ(2d,p) MCSCF/DZV(2d,p) MCQDPT/DZV(2d,p)a a
singlet Cs singlet C2ν triplet C2ν 2.25 4.29 2.29 8.77 5.47
0.0 0.0 0.0 0.0 0.0
4.59 6.09 4.59 13.5 5.81
MCQDPT/DZV(2d,p)//MCSCF/DZV(2d,p).
target is [a,d]bisbicyclo[2.1.1]hexenocyclooctatetraene (7) or a cognate (for example, 8).
Computationally, localized singlet 7 and 8 are predicted to be essentially planar with a large HOMO/LUMO gap; the precise planar form with Cs symmetry is roughly 0.6 kcal/mol higher in energy than the corresponding nonplanar C1 form.44 In the C2ν “bond delocalized” structures the HOMO and LUMO converge, allowing three possible singlet configurations to exist, with electron populations of (2,0), (0,2), and (1,1), respectively. The configuration with both electrons occupying the same orbital lies ∼17 kcal/mol higher than the Cs structure; however, the disjoint nature of the orbitals allows for the (1,1) configuration of the singlet to relieve electron repulsion and benefit from “dynamic spin polarization”.45 In 7, this stabilization is sufficient enough to drop the relatiVe energy of the C2ν (1,1) singlet to lower than that of the Cs singlet, thus predicting singlet 7 to be a planar delocalized cyclooctatetraene (Tables 2 and 3). Although hybrid DFT methods have been noted for their success in predicting singlet-triplet gaps, for example in substituted carbenes,46-49 the method remains controversial. Multireference perturbation theory provides an important computational comparison. In particular, the method used here, MCQDPT/DZV(2d,p), is known to give quantitatively accurate singlet-triplet energy splittings and the algorithm ensures that avoided crossings of states of the same symmetry are treated correctly. (45) (a) Borden, W. T.; Davidson, E. R. J. Am. Chem. Soc. 1977, 99, 4587. (b) Borden, W. T.; Iwamura, H.; Berson, J. A. Acc. Chem. Res. 1994, 27, 109. (c) Hrovat, D. A.; Borden, W. T. J. Mol. Struct. (THEOCHEM) 1997, 298-9, 211-220. (46) Das, D.; Whittenburg, S. L. THEOCHEM 1999, 492, 175-186. (47) Hu, C.-H. Chem. Phys. Lett. 1999, 309, 81-89. (48) Mendez, F.; Garcia-Garibay, M. A. J. Org. Chem. 1999, 64, 70617066. (49) Jursic, B. S. THEOCHEM 2000, 496, 83-93.
1758 J. Am. Chem. Soc., Vol. 123, No. 8, 2001
Baldridge and Siegel
Figure 2. Disjoint singly occupied orbitals of 7.
We have performed MCSCF[(8,8)] computations followed by MCQDPT corrections on 7 to evaluate the relative ordering of states. In the case of 7, the relatively low energy of the diradical C2ν form persists.
Stabilization due to dynamic spin polarization is at the core of violations of Hund’s rule,50 as pointed out by Borden.45 If applicable in the case of 7, this would mean that the triplet structure should be higher in energy than the singlet. Turning our attention to the triplet configuration of 7, computations at all levels predict a C2ν symmetric structure to be the minimum energy form. Distortion along the “bond shift” coordinate reoptimizes to the C2ν structure, supporting a single-well potential for the triplet surface. The bond lengths in 7 are close to the standard C(aromatic)-C(aromatic) length. Comparing the singlet and triplet C2ν energies, one finds that, consistent with Hrovat and Borden’s computations on the parent cyclooctatetraene,16 the triplet structure is significantly lower in energy than the (2,0) singlet of same symmetry (∆E ) 14.6 kcal/mol), but still higher in energy than the (1,1) singlet configuration (∼5 kcal/mol). The two singly occupied orbitals of 7 display disjoint nodal structures, one of the key elements in the Borden model (Figure 2). Even though the triplet C2ν structure is higher than the singlet C2ν for 7, it remains only 2.3 kcal/mol higher than the bond-localized Cs singlet, at the B3PW91/DZ(2d,p) level (50) Hund, F. Zeitschrift Physik 1925, 33, 855.
of theory.51 In the case of 8, the trends in energy among the respective triplet and singlet forms parallels that seen for 7. As a model for pure strain-induced effects, one can look to the structures and properties of 1 restricted in its CCH angles. From this procedure a control structure for 5-I, 5-II, and 7 (C2ν) is developed by replacing the annelations with hydrogens and fixing the CCH angle to that of the CCC angle in the annelated species. Computations on this series showed that the differential energetics between exo and endo forms of 5 is not substantiated by σ-angle distortion alone (∼ 0.7 kcal/mol for the control versus 32.4 kcal/mol for 5-I - 5-II). Furthermore, in the control structure versus 7 the special stabilization of the C2ν diradical is not reproduced. Both of these comparisons support the model wherein the bicyclic annelation interacts directly with the π-system and acts more than to simply constrict angles. It is our contention that this is in general true for the bicyclic annelated compounds we have studied and contradicts ideas that strain-induced bond localization dominates these systems.38 Additional support for the direct π interaction can be seen in the experimental and theoretical work on model bicyclo[2.1.1]hexene and 2,3-dimethylenebicyclo[2.1.1]hexane.41-43 In conclusion, this work demonstrates that planar localized cyclooctatetraene is a reasonable structure once the issue of angle strain is removed. The comparison of 2, 3, and 5 with distorted COT conformers reinforces our model that bicyclic[2.1.1]hexeno annelations strongly perturb the electronic structure and bond length alternation in annulenes. This especially strong perturbation of the electronic structure by bicyclo[2.1.1]hexeno annelation makes feasible the idea of “valance bond (51) Single-point computations performed on 7 at B3PW91/DZV(2df, pd)//B3PW91/DZ(2dp) showed no change in the relative energy profile of the singlet and triplet states.
Planar Delocalized Cyclooctatetraene
J. Am. Chem. Soc., Vol. 123, No. 8, 2001 1759
frustration” in the design of 7 and 8. The delocalized diradicaloid state of 7 and 8 are predicted to be lower in energy than the localized closed-shell state. On the basis of these predictions, we anticipate the synthesis and isolation of a planar “delocalized” cyclooctatetraene in the image of 7.
for hosting him as a Meyerhoff Professor during a portion of this research time (in absentia, UCSD). A grant for supercomputer time was provided through the SDSC-National Resource Allocation Program, as well as a generous donation of computer access provided by Compaq.
Acknowledgment. This work is supported by the U.S. National Science Foundation (CHE-9904275) and the NIHNBCR (RR08605-06). K.K.B. thanks the Fulbright program for a fellowship. J.S.S. thanks the Weizmann Institute of Science
Supporting Information Available: Optimized coordinates for all the molecules calculated (PDF). This material is available free of charge via the Internet at http://pubs.acs.org. JA003383+
